Multiplication and Division, Part 1

Objective

Build fluency with division facts using units of 2, 5, and 10.

Common Core Standards

Core Standards

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• 3.OA.A.2 — Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

• 3.OA.B.6 — Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

• 3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Criteria for Success

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1. Solve division and unknown factor problems involving twos, fives, and tens by skip-counting, keeping track on their papers or on their fingers of how many twos, fives, or tens have been counted, stopping the skip-counting sequence when they reach the dividend, knowing that the number of twos, fives, or tens that they counted is the solution.

Tips for Teachers

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• “For $8\times3$, you know the number of 3s and count by 3 until you reach 8 of them. For $24\div 3$, you count by 3 until you hear 24, then look at your tracking method to see how many 3s you have. Because listening for 24 is easier than monitoring the tracking method for 8 3s to stop at 8, dividing can be easier than multiplying” when using a skip-counting strategy to solve (OA Progression, p. 25). Thus, this lesson should be more accessible to students than Lesson 7.
• As a supplement to the Problem Set, students can play the first version of "What's your Number?" from the Preferred Tasks in 3.OA.4 - About the Math, Learning Targets, and Rigor by the Howard County Public School System.

Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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Problem 1

Maureen says the skip-counting sequence “10, 20, 30, 40, 50, 60” to help her solve a problem.

a. What multiplication problem might Maureen be trying to solve? How do you know?

b. What if Maureen was solving a division problem? What problem might that have been?

Problem 2

Solve.

a.   $12\div2 =$ _____

b.   _____ $=35\div 5$

c.   $90\div 10=$  _____

d.   _____ $\times 5 = 45$

e.   $2 \times$ _____ $=16$

Discussion of Problem Set

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• I think the answer in #3f is 8. Do you agree or disagree? What mistake did I make?
• What do you notice about #11a and #11d? What do you wonder?
• Is division commutative? How do you know?

1.   $90 \div 10 =$ _____                                    2.   ____ $\times 2 = 8$                                     3.   $40 = 5\times$ _____